Other
Exam style q
- Course
- Institution
A bunch of various exam style q which are not available out there and gives a glimpse of real exams obtained as per varying difficulty
[Show more]
Seller
Follow
sanjanasshetty2804
Content preview
Name: _______________________________________________Edexcel A Level Further Mathematics : Further Mechanics
Elastic strings and springs and elastic energy
Date:
Time:
Total marks available:
Total marks achieved: ______
Questions
,Q1.
A spring of natural length a has one end attached to a fixed point A. The other end of the spring
is attached to a package P of mass m.
The package P is held at rest at the point B, which is vertically below A such that AB = 3a.
After being released from rest at B, the package P first comes to instantaneous rest at A.
Air resistance is modelled as being negligible.
By modelling the spring as being light and modelling P as a particle,
(a) show that the modulus of elasticity of the spring is 2mg
(5)
(b) (i) Show that P attains its maximum speed when the extension of the spring is
a
(ii) Use the principle of conservation of mechanical energy to find the maximum speed, giving
your answer in terms of a and g.
(6)
In reality, the spring is not light.
(c) State one way in which this would affect your energy equation in part (b).
(1)
(Total for question = 12 marks)
Q2.
Figure 5 represents the plan view of part of a smooth horizontal floor, where RS and ST are
smooth fixed vertical walls. The vector is in the direction of i and the vector
, is in the
direction of (2i + j).
A small ball B is projected across the floor towards RS. Immediately before the impact with RS,
the velocity of B is (6i – 8j) m s–1. The ball bounces off RS and then hits ST.
The ball is modelled as a particle.
Given that the coefficient of restitution between B and RS is e,
(a) find the full range of possible values of e.
(3)
It is now given that e =
and that the coefficient of restitution between B and ST is
(b) Find, in terms of i and j, the velocity of B immediately after its impact with ST.
(7)
(Total for question = 10 marks)
Q3.
A particle P, of mass m, is attached to one end of a light elastic spring of natural length a
and modulus of elasticity kmg.
The other end of the spring is attached to a fixed point O on a ceiling.
The point A is vertically below O such that OA = 3a
The pointB is vertically below O such that OB =
a
The particle is held at rest at A, then released and first comes to instantaneous rest at the point
B.
(a) Show that k =
(3)
(b) Find, in terms of g, the acceleration of P immediately after it is released from rest at A.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller sanjanasshetty2804. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.18. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
56326 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now